# Study of Cullum's and Willoughby's Lanczos method for Wilson fermions

## TL;DR

This paper evaluates Cullum and Willoughby's Lanczos method for computing spectra of Wilson fermions in lattice gauge theories, analyzing its reliability, convergence, and computational cost across various lattice sizes.

## Contribution

It provides a detailed study of the Lanczos method's effectiveness and computational behavior for Wilson fermions on different lattice volumes, including spectral density and determinant calculations.

## Key findings

- Method remains reliable on larger lattices
- Cost grows approximately with the square of lattice volume
- Complete spectra obtained for lattices up to 8^3×12

## Abstract

The Lanczos method of Cullum and Willoughby is studied for euclidean Wilson fermions in quenched and unquenched SU(2) gauge fields on lattices of volume ranging from $4^4$ to $16^4$. The method is reliable even on larger lattices, but its cost for the computation of a given fraction of the spectrum grows (approximately) with the square of the lattice volume. We investigate the convergence behaviour and show that it is closely linked with the local spectral density. Complete spectra are determined on lattices up to $8^3 \cdot 12$. For configurations where all eigenvalues are computed, we give numerical values for the fermionic determinants and results for spectral densities. Determinants are also given for staggered fermions whose quenched and unquenched spectra were studied in a previous publication.

---
Source: https://tomesphere.com/paper/hep-lat/9509071